Analysis of non-linear discrete event dynamic systems in (min, +) algebra

Abstract

Under the name discrete event dynamic systems are grouped some systems whose dynamic behaviour cannot be described by differential equations. This class of systems includes many industrial systems, for which we study the flow entities (material, resources). This paper deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGM). These models do not admit a linear representation in (min,+) algebra. This non-linearity is due to the presence of the weights on arcs. To mitigate this problem of non-linearity and to apply some basic results used to analysis the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min,+) linear model.